Hover Performance of a Cycloidal Rotor for a Micro Air Vehiclesites.utexas.edu/sirohi/files/2017/07/010_parsons07_jahs.pdf · 2017. 7. 24. · much higher viscous drag than conventional

Hover Performance of a Cycloidal Rotor for a Micro Air Vehicle

Jayant Sirohi∗ Eric Parsons Inderjit ChopraAssistant Research Scientist Graduate Research Assistant Alfred Gessow Professor and Director

Alfred Gessow Rotorcraft Center, Department of Aerospace Engineering, University of Maryland, College Park, MD

In recent years, interest has been growing in a new class of very small flight vehicles called micro air vehicles (MAVs). Hovercapability is highly desirable with respect to the mission requirements of these vehicles. Due to the small size of MAVs and thelow Reynolds number regime in which they operate, scaling down conventional rotorcraft configurations to the MAV scalemay not yield optimum performance. Unconventional vehicle configurations can be explored to realize high endurance hovercapable MAVs. This paper investigates the hover performance of a small-scale cycloidal rotor to determine its viability foruse in a micro air vehicle. A 6 inch diameter prototype rotor was constructed and tested to determine the effects of number ofblades, blade pitch angle, and rotational speed on thrust output and power requirements. Pressure distribution was measuredto obtain insight into the downwash and flow through the rotor. An analytical model, using a combination of vertical axiswind turbine theory and an indicial solution for the aerodynamic response was developed to predict rotor performance, andwas validated with the experiments. The performance of the cycloidal rotor was compared to that of a conventional rotorof the same diameter in terms of power loading. Based on the analytical model and the experimental results, a conceptualdesign of an MAV utilizing cycloidal propulsion was developed. The conceptual cyclo-MAV utilizes two cycloidal rotors,providing thrust, propulsion, and control. Complete vehicle weight is envisaged to be 240 g, with two three-bladed rotors ofsix inches diameter.

Nomenclature

AR aspect ratio of bladea location of pivot point of the airfoil measured

from mid-chord, aft positiveb semi-chord of airfoilbr span of the cycloidal rotorCc

L circulatory lift coefficient of bladeCc

Lαcirculatory lift curve slope of blade

c airfoil chordd rotor diameterdA elemental area of actuator disk used in momentum analysisdT thrust of actuator disk elemente Oswald span efficiency factorFnorm force produced by a blade normal to its circular path around the

rotor azimuthFres resultant force of Fx and Fz

Ftan force produced by a blade tangential to its circular path aroundthe rotor azimuth

Fx force produced by a blade in the horizontal (x) directionFz force produced by a blade in the vertical (z) directionk reduced frequencyl total lift of the airfoillc circulatory lift of the airfoilMa aerodynamic moment about the pitching axis of the airfoilMtot total moment about the pitching axis of the airfoilm mass flow rate

∗Corresponding author; email: [email protected] received May 2006; accepted March 2007.

Nb number of bladesP power required by the rotorQ rotor torqueR rotor radiusRe Reynolds numbervd induced velocity, downstream half of rotorvu induced velocity, upstream half of rotorV∞ far upstream velocity of upstream half of rotorw far wake induced velocity of upstream half of rotor and far

upstream velocity of downstream half of rotorw∞ far wake induced velocity of downstream half of rotorα angle of attackαdw induced angle of attackδ Dirac functionθ blade pitch angle measured with respect to the tangent of the

blade’s circular path around the rotor azimuthθmax amplitude of the blade pitch oscillationφ phase angle of eccentricity of the rotor measured

counterclockwise from the negative z axisφs Wagner’s function blade position around the azimuth of the rotor measured

counterclockwise from the negative z axis rotational speed of cycloidal rotorω angular velocity of blade about pivot point

Introduction

Recent interest in micro air vehicles (MAVs) has developed, in part,due to the changing needs of the military as the battlegrounds of the

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future move to restricted, highly populated urban environments whereconventional aircraft lose much of their utility. Hover capability is highlydesirable in these environments for missions such as surveillance. Sev-eral hovering MAVs based on scaled down single main rotor and coaxialhelicopter configurations have been successfully built and flight tested(Refs. 1, 2). These MAV scale rotors typically operate in the Reynoldsnumber range from 10,000 to 100,000. Consequently, they experiencemuch higher viscous drag than conventional helicopter rotors. As a re-sult, MAV scale rotors suffer from an inherent limitation in aerodynamicefficiency, which translates into poor endurance (Ref. 3). By careful de-sign of rotor blade geometric parameters such as solidity, twist, taper,camber, and tip shape (Refs. 2, 4) the maximum figure of merit achievedto date for a rotor of diameter 9 inches is around 0.64, and for a rotor ofdiameter 6 inches is around 0.55 (Ref. 5), at a tip Reynolds number of40,000. In comparision, a conventional helicopter rotor with a figureof merit of 0.64 is considered poor in terms of aerodynamic efficiency. Infact, most of the modern helicopter rotors have a figure of merit of about0.75–0.8 (Ref. 6).

An MAV based on a cycloidal rotor is proposed as an alternative tohelicopter based MAVs. The concept of cycloidal propulsion is quite old,but it has remained relatively obscure until recently. Kirsten (Ref. 7) in-vestigated cycloidal propulsion at the University of Washington in the1920s. He constructed a large cycloidal propeller and investigated its usein air vehicles. However, he subsequently began to explore applicationsof the cycloidal rotor in marine systems, and today, these are used exten-sively in tug boats, to provide them with the maneuverability necessaryto operate in confined harbors. In the 1930s, Wheatley (Refs. 8, 9) devel-oped a simplified aerodynamic theory of a cyclogiro rotating wing andconducted wind tunnel tests on a large four-bladed prototype rotor withdiameter and span of 8 feet. The blades incorporated a NACA 0012 airfoilprofile and had a chord of 0.312 ft. Significant thrust levels were mea-sured but poor agreement between theory and experiment was achievedmainly due to incomplete knowledge of forces on oscillating airfoils.Cycloidal rotors have also been proposed for use on airships (Refs. 10,11) as they can result in significantly increased maneuverability.

More recently, Gibbens et al. (Ref. 12) proposed a UAV configu-ration with a gross weight of 600 lb, having two cycloidal rotors toproduce lift and propulsion. A full scale experimental setup was con-structed to measure the thrust produced and power consumed by a singlecycloidal rotor. The rotor had a span of 4 ft, a diameter of 4 ft and sixblades of chord 1 ft with a NACA 0012 airfoil. A maximum power load-ing of 10.88 lb/HP was recorded, and the rotor operated at a maximumReynolds number of around 730,000. A significant lack of noise was ob-served during operation. McNabb (Ref. 13) developed a computer modelfor this cycloidal rotor and compared the predictions with experimentalresults.

Kim et al. (Ref. 14) experimentally investigated the performance ofa cycloidal rotor with a span of 0.8 m. The blades used a NACA 0012airfoil, with a chord of 0.15 m. Rotor thrust and torque were measured,and the effect of blade pitch angle, rotor radius, and number of blades werestudied up to a rotational speed of 600 rpm, corresponding to a Reynoldsnumber of around 260,000. It was observed that thrust was proportionalto the square of rotational speed, and power was proportional to the cubeof rotational speed. A maximum power loading of around 12 kgf/HPwas observed at low thrust levels, which asymptotes to around 5 kgf/HPat high thrust. An analysis was also conducted using commercial CFDsoftware to predict rotor characteristics. Yun et al. (Ref. 15) designed aVTOL UAV with cycloidal rotors intended to have a take-off weight of50 kg. Hwang et al. (Ref. 16) optimized the aerodynamic and structuraldesign of a VTOL UAV using four cycloidal rotors of radius 0.85 m, aswell as designed a micro-scale cyclocopter with two cycloidal rotors ofradius 0.2 m.

Vertical axis windmills (VAWTs) experience a motion similar to cy-cloidal rotors although they generally possess fixed pitch blades. A largebody of work has been conducted in developing aerodynamic perfor-mance prediction methods for these windmills (Refs. 17–19). In addi-tion, a small percentage of VAWT designs incorporate variable bladepitch similar to the cycloidal blade system.

The cycloidal blade system may be considered as a horizontal rotarywing, with its blade span parallel to a horizontal axis of rotation. As theblades rotate around the azimuth, their pitch angle is varied periodically.Each spanwise blade element operates at about the same conditions—velocity, Reynolds number, angle of attack, centrifugal force—and thuscan be designed to operate at its optimum efficiency. Due to the highlyunsteady flow field and the constant angle of attack over the entire spanof the blade, a cycloidal rotor may exhibit better performance than a con-ventional rotor at the MAV scale. Figure 1 shows the approximate powerloading of several production helicopters as well as a few experimentalcycloidal rotors. It can be seen that in general, cycloidal rotors exhibita higher power loading than conventional helicopters. This improvedpower loading is very attractive for exploring cycloidal propulsion on theMAV scale. In addition, a cycloidal rotor has the ability to change thedirection of thrust almost instantly, resulting in good maneuverability atlow freestream velocities, which is highly desirable for MAV operationin confined areas.

Although existing literature seems to show that the cycloidal rotoris superior to a conventional rotor in terms of power loading, it is un-clear how they compare with respect to a constant linear dimension. Thisinformation is critical to the choice of a configuration for an MAV. Inaddition, other metrics such as hover figure of merit must be investi-gated, with which a meaningful comparison can be made. The studiesdescribed above involved testing of large-scale models, at relatively highReynolds numbers. It remains uncertain how the design would translateto an MAV-scale vehicle, operating at a maximum Reynolds number ofless than 20,000. None of the previous studies had a comprehensive anal-ysis that matched well with their experimental results and could be usedas a preliminary design tool. The present research aims to address someof these issues.

The primary objective of the present research was to determinewhether a cycloidal rotor configuration is a viable means of propulsionfor an MAV. A secondary objective was to develop a simple analyticaltool for predicting the performance of a cycloidal rotor and to validatethe analysis with experiments. These objectives are carried out by char-acterizing the performance of a small-scale cycloidal rotor of diameterand span of 6 inches. Performance of the rotor was studied by deter-mining thrust and torque of the rotor as a function of number of blades,blade pitch angle and rotational speed. A theoretical model was devel-oped incorporating unsteady aerodynamic effects, and was validated withexperiments. An investigation of the flow field around the model rotorwas conducted by measuring the pressure distribution below the rotor andacross its cross-section. The efficiency of the cycloidal rotor was com-pared with that of a conventional rotor of the same diameter, both in termsof power loading and figure of merit. Finally, the analysis was used toperform a preliminary design of an MAV utilizing cycloidal propulsion.Weights and constraints were applied using CAD software to determineif the rotors could provide the necessary thrust and if the construction ofthe vehicle on the MAV scale was feasible.

Operating Principle

A cycloidal rotor consists of several blades that rotate about a hor-izontal axis that is perpendicular to the direction of flight (Fig. 2).Blade span is parallel to the axis of rotation. The pitch angle of eachof the blades is varied such that it changes periodically about the

JULY 2007 HOVER PERFORMANCE OF A CYCLOIDAL ROTOR FOR A MICRO AIR VEHICLE 265

12.6

12.5

10.9

10.1

9.12

8.7

9.4

8.2

6.8

6.7

6.6

6.4

6.2

5.8

5.7

5.2

4.9

4.3

3.7

2.8

0 2 4 6 8 10 12 14

Kirsten 1923

Wheately 1935

Bosch 1998

Hwang 2006 (UAV)

Yun 2004

Hwang 2006 (MAV)

Sirohi 2005 (MAV)

S 65

MD 500

Bell 212

SA 342

CH 47

UH 60

MI 24

AH 64

SA 367

MI 28

V22

EH 101

KA 50

Power loading, lb/HP

Conventional rotor

Cycloidal rotor

Fig. 1. Comparison of power loading of conventional rotors and cycloidal rotors (adapted from Ref. 12).

Fig. 2. Cycloidal rotor configuration.

airfoil quarter-chord as the blade moves around the azimuth of therotor.

Each of the blades produces a lift and a drag force. Blades at thetop and bottom positions produce an almost vertical net force, whilethose at the sides produce small lateral forces because of their reducedangle of attack. Figure 3 shows a cross-section of a six-bladed cycloidalrotor rotating with an angular velocity . The horizontal and verticalcomponents of the force acting on each blade is also shown. It can beseen that the sum of the horizontal components is zero, resulting in anet vertical thrust. In addition, the amplitude and phase of the maximumblade pitch angle may be changed, resulting in a change of the magnitudeand direction of the net thrust vector of the rotor.

Ω

Fig. 3. Thrust vectors at each blade cross-section.

Experimental Setup

Experiments were performed on a prototype cycloidal rotor to obtainan understanding of the flow field around the rotor as well as to carefullymeasure the performance of the rotor in terms of thrust produced andpower consumed. Two separate experimental setups were constructed.The first setup was dedicated to investigating the flow field by measuringthe pressure distribution in the downwash and along the cross-sectionof the rotor. The second setup consisted of a fixture with load cells tomeasure the rotor thrust, torque and rotational speed.

Prototype cycloidal rotor

A prototype cycloidal rotor was constructed with six blades and adiameter and blade span of six inches. The blades use a NACA 0010airfoil profile and have a one inch chord. The rotor could also be tested in


Table 1. Geometry of linkages used onexperimental rotor

Linkage Length (inch)

L1 2.331L2 0.180 (variable)L3 2.369L4 0.426

Fig. 4. Offset mechanism four bar linkage.

a three-bladed configuration. The main structural elements of the designconsists of two end plates, to which each of the blades is attached. Thetwo end plates are also connected to each other by a rigid shaft, and theassembly rotates around another concentric shaft.

The required blade pitch motion around the rotor is achieved by apassive mechanism and the only power required for its operation is toovercome both the friction associated with its moving components andthe inertial forces associated with the oscillatory change in pitch. Themechanism consists of both fixed and rotating parts. A shaft is offsetfrom the center of rotation of the rotor. This offset piece is fixed, and itsorientation sets the direction of the thrust vector for the rotor. Attachedto this offset piece is a bearing and a rotating disk, to which six linkagesare attached. Each of the linkages connects to the trailing edge of oneof the blades. Together, the system comprises a crank-rocker type fourbar linkage, which is used to accomplish the required change in bladepitch angle (Fig. 4). The offset piece was designed so that the blade pitchangle amplitude could be set from 0 to 40 by changing the linkagelength L2. Note that the blade pitch angle is defined at any azimuth as theangle between the mean chord line of the airfoil and the tangent to thecircular path of the airfoil at that azimuth. Another important geometricparameter is the eccentricity φ, which defines the azimuthal locationof the maximum blade pitch angle. Table 1 provides the lengths of thelinkages.

The blades for the cycloidal rotor are constructed of carbon fiber com-posite wrapped around a foam core. Note that because of the constraintthat they must operate effectively at both positive and negative angles ofattack, the symmetric NACA 0010 profile was used for the airfoils. The

5 3 1 1 3 54

3

-

-

-- - -

2

-1

0

1

2

3

4

x, in5 3 1 1 3 5

3

2

1

0

1

2

3

4

Rotor planform

Rotor shaft

y, in

Fig. 5. Definition of the coordinate axes for pressure measurement,below the rotor.

rotor was driven by a brushless motor, and all components were weighedand balanced within 0.01 g.

Measurement of flow field around the rotor

Experiments were performed to investigate the flow field around thecycloidal rotor by means of total pressure measurements, in order toobtain a physical feel of the downwash distribution and thrust productionmechanism. As some uncertainity exists in the exact flow direction, a1/16 inch diameter Kiel probe was used to measure the total pressure,because such a probe is insensitive to entry cone angles of up to 45.The goal of these experiments was to obtain a qualitative picture of theflow field around the rotor, as well as to measure the velocities in thedownwash of the rotor. The prototype cycloidal rotor was supported intwo different configurations for this testing. In the first case, the cycloidalrotor was supported on one end only, in a cantilevered condition. In thesecond case, both ends of the rotor were supported and the rotor waseffectively in a clamped–clamped condition. In both cases, the axis ofrotation of the cycloidal rotor was horizontal.

A differential pressure transducer (0–50 Pa range) was used to recordthe pressure. Pressure measurements were recorded at one-inch incre-ments in both the x and y directions (in the horizontal plane). The mea-surements were then repeated at locations of 0.5, 3, 6, and 9 inchesbelow the rotor (vertical plane). Rotational speed was kept constant at1100 rpm. Vertical movement was achieved by mounting the probes ona height gauge, with a precision of ±0.001 inch. Movement in the x andy directions was accomplished by mounting the height gauge to a twodegree-of-freedom x–y positioning stage driven by stepper motors thatallowed for movements with a precision of ±0.001 inch. The coordinateaxes used in the measurement of the downwash distribution are definedin Fig. 5. Measurements were recorded from x = −5 inch to x = 5 inchand y = −4 inch to y = 4 inch.

Measurements were also taken along the rotor flow cross-section forthe rotor in the clamped condition. The Kiel probe was located at thecenter of the blade span, and pressure measurements were recorded inthe x and z directions in one-inch increments from x = −5 inch to x = 5inch and z = −4 inch to z = 4 inch. Figures 5 and 6 define the coordinateaxes for this testing. Note that due to the geometry of the setup, thesemeasurements could be performed only outside the rotor.


-5 -3 -1 1 3 5

1

0

1

2

3

4

x, in

z, in

Rotor cross-section

-

-2

-3

-4

Fig. 6. Definition of the coordinate axes for pressure measurement,cross-section of the rotor.

Measurement of loads and power

A test rig was constructed to measure mechanical as well as electricalpower consumed by the cycloidal rotor. Figures 7 and 8 illustrate theconstruction of the test rig. The rotor is mounted on a nonrotating shaft,which runs through bearings mounted in vertical plates at each end. Eachvertical plate is mounted on a linear slide, preventing horizontal motionand minimizing friction. Each plate is attached to a load cell, which is, inturn, attached to the base. As a result, the load cells measure the verticalforce at each end of the nonrotating shaft. The sum of these forces givesthe total thrust produced by the rotor.

The drive motor is mounted on the nonrotating shaft and is connectedto the rotor by a spur gear. One end of the nonrotating shaft is attachedto a torque load cell, which is clamped to one of the vertical plates.Therefore, as the drive motor is not clamped to the base, the torque loadcell measures the total torque on the rotor system. The rotational speedof the rotor is measured by a Hall sensor.

A range of tests were performed to characterize the performance ofthe rotor. Measurements were taken at blade pitch angle amplitudes of10, 20, 30, and 40 for rotational speeds ranging from 0 to 1200 rpm.The tests, were conducted with six blades and were repeated with threeblades to determine the effect of the number of blades on the performanceof the rotor. A series of tests were also performed to determine the ef-

Fig. 7. Cycloidal rotor test setup.

Fig. 8. Torque measurement in the cycloidal rotor test stand.

fect of blade pitch angle on the direction of the resultant thrust vector.Measurements were recorded for blade pitch angles ranging from 0 to40 and eccentricity, φ, varying from −50 to 50. Rotational speed washeld constant at 800 rpm for these tests. To determine the power requiredby the rotor to overcome mechanical friction, tare tests were performedwith all blades removed. These tare tests were conducted for blade pitchangles from 0 to 40, with rotational speeds ranging from 0 to 1200 rpm.The aerodynamic power consumed was calculated by subtracting the tare(mechanical) power from the total power.

Analytical Procedure

An analytical model of a cycloidal rotor was developed to predict themagnitude and direction of thrust as well as power requirements of acycloidal rotor in hover. The goal is to develop a simple model of cy-cloidal rotor performance, based on existing momentum theory analysisof vertical axis wind turbines, for use as a design tool. To calculate theperformance of the rotor, the azimuthal position and pitch angle of eachblade must be determined. This can be calculated from the kinematics ofthe four bar mechanism used to create the pitch change. From the pitchangle of each blade and the rotor downwash, the angle of attack of eachblade can be determined. Lift and drag forces are calculated based on un-steady aerodynamics. The forces from each blade are summed to find thetotal vertical and horizontal forces for the rotor. Downwash is determined


from the resultant thrust using a modified version of momentum theoryand is used to calculate the induced angle of attack. An iterative procedureis then executed until convergence is achieved for lift and drag forces.The rotor is then rotated by an incremental amount and the process isrepeated to calculate the rotor forces as a function of azimuth.

Coordinate system

Figure 9 shows the coordinate system used for the analysis. The az-imuthal position of the blade, , is measured counterclockwise from thenegative z-axis. From Fig. 10, φ is the phase angle of eccentricity, usedto define the direction of thrust, and is measured counterclockwise fromthe negative z-axis. Blade pitch angle (θ ) is measured with respect tothe tangent of the blade’s circular path. Velocities and forces are positiveupward as well as in the direction of rotation and radially outward.

The coordinate system for the airfoil is shown in Fig. 11. The airfoilis represented as a line extending from the leading edge at chordwiselocation x = −1 to the trailing edge at x = +1. The axis of rotation, orpitching axis, for the airfoil is located at point a. The airfoil may experi-ence movement in the vertical direction, h, measured positive downward,or rotation about x = a, positive in the nose-up direction. The incidentvelocity v moves from left to right. The angle of attack α is defined as theangle between the velocity v and the instantaneous position of the airfoilchord line.

+X270o

+Z180o

Fig. 9. Definition of coordinate system for analysis.

θ

φ ψ

Fig. 10. Pitch angle definition for the cycloidal rotor.

x = +1x = +1

V

h

x = −1

Leading edge

Axis of

rotation

0

a

Trailing edge

Fig. 11. Airfoil coordinate system.

Unsteady aerodynamics

Each rotor blade experiences a highly unsteady aerodynamic environ-ment as it rotates around the azimuth. This includes the periodic oscilla-tion in angle of attack due to the pitch change mechanism, the effects ofthe previous blade wake, three-dimensional effects, and dynamic stall athigh angles of attack. Reduced frequency is defined as

k = ωb

V(1)

where b is the airfoil semi-chord, ω is the frequency of oscillation and Vis the incident velocity. The reduced frequency of the cycloidal rotor isgiven by

k = ωc

2V= c

2R(2)

Note from Eq. (2) that the reduced frequency simplifies to a geometricratio independent of rotational speed and as such, its meaning is ambigu-ous. Substituting values for the chord and radius of the present cycloidalrotor prototype results in a reduced frequency of k = 0.167. Typically,for k > 0.2, the flow is highly unsteady, and unsteady effects will beginto dominate the behavior of the airloads (Ref. 20). Therefore, unsteadyeffects are included in the present analysis.

The methodology used to arrive at the forces in the present analysisrelies on a time domain formulation. Wagner’s function is used to solvefor the indicial lift on an airfoil undergoing an incremental change in angleof attack. Note that the application of Wagner’s function to the presentproblem is an approximation, as the wake from the trailing edge of theairfoil is not planar. However, this assumption is considered acceptablefor the present analysis.

The variation in lift coefficient for a step change in angle of attack asgiven in Ref. 20 is

Cl (t) = πc

2Vδ(t) + 2παφ(s) (3)

where δ(t) is the Dirac delta function, α is the angle of attack and φ(s)is the indicial response. Once the response is found, the unsteady loadsresulting from changes in angle of attack may be found through super-position of the responses, accomplished through a numerical solution ofthe convolution integral. Assuming the indicial response is known, thesystem output y(t) is given by

y(t) = f (0)φ(t) +t∫

0

d f

dtφ(t − σ ) dσ (4)

where f (t) is the forcing function. For this problem, the forcing functionis the angle of attack of the blade, Wagner’s function is the indicialresponse, and the lift is the output. Although Wagner’s function is knownexactly for incompressible flow, its formulation is not convenient for ananalytical solution. Instead, an exponential approximation, provided byJones (Ref. 20), is used to simplify the problem.

φ(s) ≈ 1.0 − 0.165 e−0.0455s − 0.335 e−0.3s (5)


The circulatory part of lift for a rigid airfoil starting from rest at t = 0inch response to a variation in angle of attack is given by

lc(s) = 1

2ρV 2 SClα

α(0)φ(s) +

s∫so

dα(σ )

dsφ(s − σ ) dσ

(6)

Including noncirculatory (apparent mass terms), the total lift is given as

l(s) = Clα ρV 2b

α(0)φ(s) +

s∫0

dα(σ )

dsφ(s − σ ) dσ

+ πρb2(V α − abα) (7)

per unit span, assuming V is constant, where a is the location of the pitchaxis and b is the airfoil semi-chord (Ref. 21). For this case, the pitchaxis is located at the quarter chord of the airfoil (a = − 1

2 ). This equa-tion is solved numerically for discrete values of time using a recurrencealgorithm (Ref. 22).

Drag is calculated as the sum of the profile and induced components,

D = 1

2ρV 2 S

(CDo +

(Cc

L

)2

π ARe

)(8)

where CDo is the profile drag coefficient for the airfoil and CcL is the

circulatory component of the unsteady lift given by Eq. (6). Empiricaldata from Refs. 23 and 24 were used for the lift curve slopes as well asthe profile drag coefficients, as these quantities have a strong dependenceon Reynolds number. The data used for the present work are based on aNACA 0012 wing with an aspect ratio of six at a Reynolds number of20,700. Note that the maximum Reynolds number of the present cycloidalrotor is approximately 17,000. The Oswald span efficiency factor is rep-resented as e, and a value of e = 0.95 was assumed as an initial guess.Although this method of determining drag is not typical, it provides anapproach in which to directly incorporate empirical data relevant to thepresent work.

The moment of the airfoil about its pitching axis, may be derived ina similar manner as

Ma = πρb2

[−V b

(1

2− a

)α − b2

(1

8+ a2

)α

]

+ CLαρV b2

(a + 1

2

) [α(0)φ(s) +

s∫so

dα(σ )

dsφ(s − σ ) dσ

](9)

Kinematics of the blade pitch mechanism

The above equations are dependent on α, α, and α , which respectivelyrepresent the angle of attack, angular velocity, and angular accelerationof the blade about its pitch axis (quarter-chord). The variation of bladepitch angle as a function of azimuth can be derived by examining thekinematics of the blade pitch mechanism. The blade pitch angle can beidealized as a simple sinusoidal function, given by

θ = −θmax sin( − φ) (10)

where φ is the angle of eccentricity of the offset link and is the positionof the blade around the azimuth. The angle of attack may be found bysubtracting the induced angle of attack, αdw , from the blade pitch angle.

α = θ − αdw = −θmax sin(t − φ) − αdw (11)

4

2

L2

(driving)

4

3

A

B

C

D

L3

L1 (fixed)

L4

Fig. 12. Generic four bar linkage.

The angular velocity and acceleration, are the first and second derivativesof this function, respectively:

θ = −θmax cos(t − φ) (12)

θ = θmax2 sin(t − φ) (13)

The pitch change mechanism does not produce a pure sinusoidal vari-ation in blade pitch angle. This difference also affects the angular velocityand acceleration, which influence the noncirculatory components of lift.Therefore, it is necessary to calculate the exact kinematics of the pitchchange mechanism to achieve accurate results. The mechanism in theexperimental rotor utilizes a passive four bar mechanism to accomplishthe blade pitch change. The various configurations of this type of link-age system may be found in a wide variety of mechanics or kinematicstextbooks (Ref. 25). Figure 12 illustrates a generic four bar linkage. LetL1, L2, L3, and L4 denote the lengths of the four linkages, with L1 be-ing the fixed linkage. Angles θ2, θ3, and θ4 give the angular positions ofL2, L3, and L4, respectively, and are measured counterclockwise fromthe horizontal plane. The diagonal, denoted by χ , runs from point B topoint D. The angle from χ to L3 is , while β is the angle from χ toL1. L2 is considered the driving linkage, and as such its angular posi-tion, θ2, is known. Note that this is a simplifying assumption, as in thecase of the experimental mechanism, L2 is in the fixed frame of refer-ence, and L1, L3, and L4 are in the rotating frame. The procedure toobtain the kinematics of the mechanism involves examining the trianglesABD and BCD in all configurations of the mechanism, assigning vectorsto each link and solving for the angles and rotational velocities of thelinks.

The angular velocity of link L4, which is the blade, can be obtainedas

ω4 = r2ω2 sin(θ3 − θ2)

r4 sin(θ4 − θ3)(14)

Assuming the cycloidal rotor is not accelerating (α2 = 0), the angularacceleration is found as

α4 = r3ω23 + r2ω

22 cos(θ2 − θ3) + r4ω

24 cos(θ4 − θ3)

r4 sin(θ3 − θ4)(15)

All angles, velocities, and accelerations are positive when measured coun-terclockwise. Thus, from the geometry of the linkage system, all the nec-essary terms may be determined as a function of θ2. Figure 13 comparesthe actual blade pitch angle (θ4), velocity (ω4), and acceleration (α4) of themechanism used in the experimental rotor to an ideal motion in whichthe blade pitch angle varies sinusoidally with a magnitude of 25. Notethat there is a small difference between the blade pitch angle variationand a pure sinusoid. This difference is accentuated in the time derivativesof blade pitch angle.

In addition, the maximum pitch angles of the four bar linkage arenot exactly ±25. The linkage has a slightly larger pitch angle at = 0

(θ = −26.11), and a slightly smaller one at = 180 (θ = 24.07). This


0 50 100 150 200 250 300 350

0

20

40

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de p

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angl

e (d

eg)

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2000

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ocit

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eler

atio

n(a

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rd)

(deg

/ s2 )

Azimuthal location around rotor (deg)

Four-bar linkageSinusoidal

×

Fig. 13. Actual and ideal motion of blade pitch mechanism.

difference between the upper and lower pitch angle escalates as the max-imum pitch angle increases, and is an inevitable product of using a fourbar linkage. From Fig. 13, it can be seen that there is also a phase lagof approximately 10 between the sinusoidal and actual blade motions.The phase lag changes with the maximum blade pitch angle and is againa product of the four bar linkage.

Calculation of downwash

Once the blade positions are determined from the linkage kinematics,the induced angle of attack and effective angle of attack are calculated.The calculation of the downwash, and consequently, the induced angleof attack, is key to predicting the aerodynamic loads on the rotor. Theinteraction of each blade with its neighbors can be taken into accountusing cascade aerodynamics. This depends on the ratio of blade chordto blade spacing, which is commonly referred to as the “solidity” of thecascade, as well as on the Reynolds number (Refs. 26–28). Compressorstypically have solidities of 1.0 to 1.5. The experimental cycloidal rotorin the six-bladed configuration has a solidity of 0.318. With only threeblades, the solidity is half this value, or 0.159. At this value of solidityand at the Reynolds number of operation of the prototype cycloidal rotor,any cascade effects are expected to be weak, and are neglected in thepresent analysis.

The method of analysis employed to analyze the flow field around thecycloidal rotor is based on momentum theory, where the aerodynamicforces on the rotor are equated to the time rate of change of momentumthrough the rotor. This theory is based on the assumption that the inducedvelocity is constant along the blade chord and blade span. This method ofanalysis is similar to those used in the study of vertical axis wind turbines(VAWTs) (Ref. 29). Depending on the complexity of the problem and theaccuracy necessary for the analysis, the models may further be classifiedinto four types, shown in Fig. 14, where induced velocities are representedby u.

For the present analysis, an adaptation of double-multiple streamtubemethod was employed. In this model, the flow through the rotor issubdivided into a number of streamtubes, aerodynamically independent

from one another and each with different induced velocities at theupstream and downstream halves of the volume swept by the rotor.Each streamtube intersects the rotor twice, once on the upstream sideand again on the downstream side, as shown in Fig. 15. At each of theintersections, the rotor is represented by an infinitesimally thin actuatordisk. Across each of these disks there is a pressure difference capable ofgenerating axial momentum in the direction perpendicular to the disk.The induced flow passes through the actuator disks in a radial directionand is then deflected downward vertically. It is assumed that the steadyvalue of downwash velocity is achieved within the rotor, and the wakevelocity of the upper actuator disk is used as the free stream velocity forthe lower disk (similar to a co-axial rotor system). Figure 15 illustratesthe flow model used for the analysis. This flow model can be furthersimplified into an equivalent actuator disk model as shown in Fig. 16.

From basic momentum theory, expressions for the downwash veloc-ities at each actuator disk can be derived as

w = 2vu sin (16)

vd = −1

2w ±

√w2

4− T

2ρd Acos (17)

where the thrust of the upper actuator disk is given by T = mw. Theinduced velocities vu and vd are implemented in the program through aniterative scheme until convergence occurs. Note that an assumption ismade in this flow model that the two actuator disks in each streamtubeproduce the same thrust. As such, it should be recognized that this is atentative flow model, and has not been validated experimentally.

Rotor forces and moments

Lift and drag forces on each blade are first resolved into componentsnormal and tangential to the cycloidal rotor motions:

Ftan = L sin α + D cos α (18)

Fnorm = L cos α − D sin α (19)


uu

Rotor flightpathu

ud

ud1

ud2

ud3

uu1

uu2

uu3

u1

u2

u3

(a) Single streamtube (b) Multiple streamtube

(c) Double streamtube (d) Double-multiple streamtube

Fig. 14. Streamtube models.

dT

Vu

V

w

w

Actuator

disk

Vd

dT

8

8

Fig. 15. Flow model used for hover analysis.

where α is the angle of attack of each blade. The forces are now trans-formed into the x–z coordinate system (horizontal and vertical directionin relation to the cycloidal rotor). From Fig. 17, the transformation equa-tions are found to be

Fx = Fnorm cos(θ − 90) − Ftan sin(θ − 90)

=⇒ Fx = Fnorm sin θ + Ftan cos θ (20)

Fz = Fnorm sin(θ − 90) + Ftan cos(θ − 90)

=⇒ Fz = Ftan sin θ − Fnorm cos θ (21)

By summing these total forces over an entire rotation, the averageforces in the x and z directions may be determined. Total thrust producedby the cycloidal rotor per blade is given by

Fres =√

F2x + F2

z (22)

Upstream

wV Vu Vd

w

Actuatordisk

Actuatordisk

Equilibrium

Downstream

8

8

Fig. 16. Streamtube replaced by two tandem actuator disks.

˚

Fz

˚ Fx

Ftan

Fnorm

Fig. 17. Force components in x–z coordinate system.


Fig. 18. Downwash distribution 3 inches below the cycloidal rotoraxis at 1100 rpm, cantilevered condition.

The total torque about the rotor axis is given by

Q =∑

Number of blades

Ftan R + Mtotα

(23)

Power required by the rotor is obtained by

P = Q (24)

Results and Discussion

Experiments were performed on the prototype cycloidal rotor to ob-tain a physical insight of the flow through the rotor as well as to obtainquantitative measurements of the performance of the rotor. As describedabove, the flow was visualized by means of pressure measurements andthe loads were measured on an instrumented test rig. The pressure mea-surements were performed on a six-bladed rotor in cantilevered as wellas clamped–clamped support conditions. The load measurements werecarried out on a three-bladed and a six-bladed rotor, both in the clamped–clamped support condition.

Pressure measurements

Figure 18 illustrates the downwash at 3 inches (1/2 rotor diameter)below the cantilevered prototype rotor. The outline shows the position ofthe cycloidal rotor, rotating clockwise (toward the left side of the page).The downwash at 9 inches below the rotor is shown in Fig. 19. Notethat the induced velocity distribution appears shifted toward the fixedend of the setup. This is undesirable as it is known that a nonuniformdownwash distribution results in poor aerodynamic efficiency. It wassurmised that vibrations in the rotor, in large part because of the flexibilityof the cantilevered support, were the cause of this phenomenon.

The rotor was then tested with both ends clamped to investigate theeffect of the support flexibility. Figure 20 illustrates the downwash distri-bution in the clamped condition. It can be seen that the flow is much moreuniform than in the case of the cantilevered condition. This indicates thatflexibility in the cantilevered support was the main cause of the nonuni-formity in the downwash. The results of these pressure measurements isdirectly applicable to the implementation of the cycloidal rotor on a flightvehicle. While the cantilevered condition is the most attractive in termsof flight vehicle configuration, it should be kept in mind that the supportshould be as rigid as possible to obtain a favorable downwash distribution.

All subsequent data reported in this paper were obtained from thecycloidal rotor in the clamped–clamped condition. Figure 21 shows a

Fig. 19. Downwash distribution 9 inches below the cycloidal rotoraxis at 1100 rpm, cantilevered condition.

Fig. 20. Downwash 3 inches below cycloidal rotor, clamped conditionat 1100 rpm.

cross-section of the flow measured at the mid-span of the rotor. Theinduced airflow through the top of the rotor is fairly uniform. Note thatthe inflow is greatest in the lower left quadrant of the rotor, and is sweptin the direction of rotation to the right. Consequently, the resultant thrustvector of the cycloidal rotor is deflected slightly from the vertical.

Rotor thrust and power

The measured rotor thrust and power are expressed in terms of nondi-mensional parameters. The nondimensionalization is carried out withrespect to a rotor reference area and the rotor blade tip velocity. Forexample, the rotor thrust coefficient is

CT = T

ρ(πbrd)(R)2(25)

where br and d are the length and diameter of the cycloidal rotor respec-tively, and T is the thrust (z-force). Note that πbrd is the swept area ofthe blades, and is equal to the total area of the actuator disks used in thederivation of the streamtube theory. The power coefficient is defined in asimilar manner as

CP = P

ρ(πbrd)(R)3(26)

The vertical force is plotted against rotational speed in Fig. 22for the six-bladed configuration, and in Fig. 23 for the three-bladed


Fig. 21. Cross section of flow through cycloidal rotor at 1100 rpm.

0 200 400 600 800 1000 1200 14000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

RPM

CT

Theory, pitch = 10 o



Experiment, pitch = 10 o





Fig. 22. Comparison of theory and experiment for a six-bladed rotor,z-force vs. rpm.

0 200 400 600 800 1000 1200 14000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

RPM

CT

Theory, pitch = 10o

Theory, pitch = 20o

Theory, pitch = 30o

Experiment, pitch = 10o



Theory, pitch = 40o


Fig. 23. Comparison of theory and experiment for a three-bladedrotor, z-force vs. rpm.

configuration. Theoretical predictions are also shown for both cases. Notethat for the present rotor geometry, at a rotational speed of 1000 rpm, acoefficient of CT = 0.1 corresponds to a thrust of approximately 0.57N (58 g). It can be seen that the experimental data agree well with thepredicted values for the three-bladed case. However, for the six-bladedconfiguration, the model significantly overpredicts the experimental re-sults, especially for high pitch angles. This discrepancy may be due toflow interference between the blades in the six-bladed configuration.With six blades, there are approximately three chord lengths before thenext blade hits the wake of the previous blade. The flow is still highlyunsteady, and may have a profound effect on the impinging blade. It isprobable that the assumption made in the analytical model that cascadeeffects between the blades are negligible may not be accurate.

An important detail to note is that the configuration with six bladesdoes not produce twice the thrust of the three-bladed case. The bladeson the downstream half of the rotor, from = 270 to 90, see a sig-nificant downwash from the upstream blades. This results in an increasein induced velocity and a reduction in lift produced by the downstreamblades. Thus, doubling the number of blades does not produce twice thelift. As blade pitch angle exceeds the static stall angle for the airfoil, thereis no drop in thrust, with the implication that the rotor is not experienc-ing a stalled flow condition. This remains true even as the pitch anglereaches 30 and even 40. There are two effects that may contribute tothe unusually high pitch angle that the rotor can operate at without stall.First, the downwash through the rotor is significant, and this inducedinflow would significantly decrease the effective blade angle of attack,particularly at = 0 and 180, where pitch angle is the largest. Anotherpossible contributing factor may be the occurrence unsteady aerodynamicphenomenon. This would result in a delay in flow separation to a higherangle of attack than typically seen in static stall, and as a result of this,the airfoil is able to achieve higher lift than would be possible in a staticsituation.

Pitch eccentricity

Referring to Figs. 4 and 12, the maximum blade pitch angles forthe offset mechanism will occur when linkages L2 and L3 are parallel.However, the angle, θ2, at which this takes place will vary depending onthe desired maximum pitch angle. Therefore, to simplify data acquisitionand maintain consistency in the measurements, the rotor was positionedsuch that L2 was always vertical. Thus, from Fig. 24, the maximumblade pitch angles do not appear at = 0 and 180, but at a phase lagapproaching 10 with respect to direction of the offset. This results in ahorizontal force produced by the rotor.

To determine the phase lag, or eccentricity, at which the maximumvertical thrust occurs, a series of experiments were conducted. Eccen-tricity is defined such that it is equal to zero when the offset for thepitch mechanism occurs at = 180. This is the position in which thethrust measurements shown in Figs. 22 and 23 were recorded. Note thatat this condition, the rotor is thrusting toward the ground, eliminating anypossibility of ground effect.

Figure 25 plots the experimental measurements as well as the pre-dicted values for various eccentricity locations, for the six-bladed con-figuration. Note that if the eccentricity is shifted by 180, the rotor thrustwould be in the opposite direction with the same magnitude. It can beseen that the results agree very well with the predictions. As blade pitchangle is increased, the location of maximum thrust changes. From themodel, for pitch angles of 0, 10, and 20, maximum thrust occurs veryclose to an eccentricity of zero. However, at 30 pitch angle, maximumthrust occurs at an eccentricity of +9 (counterclockwise in Fig. 24), andat 40 it shifts to +15.


Ω

+X

270o

Location of maximum

blade pitch angle

Location of maximum

blade pitch angle

Movement of offset

mechanism −X90o

+Z

180o

−Z

ψ = 0o

Eccentricity=10o

10o

Fig. 24. Relationship between pitch angle and offset mechanism.

−60 −40 −20 0 20 40 600

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Eccentricity (deg)

CT

Pitch 40oExperimentTheory

Pitch 30o

Pitch 20o

Pitch 10o

Fig. 25. Vertical force vs. offset eccentricity for six-bladed rotor.

Rotor power

The power consumed by the rotor is the summation of power re-quired to overcome the aerodynamic forces as well as the power requiredto overcome mechanical friction and inertial forces in the mechanism.

In order to assess the efficiency of the cycloidal rotor concept, and tocompare it quantitatively with the efficiency of a conventional rotor, theaerodynamic power of both configurations must be compared. This canbe obtained by performing a tare test on the cycloidal rotor. The tare testis performed by removing the blades from the cycloidal rotor and mea-suring the torque required to spin it over the entire range of rotationalspeeds. This gives a measure of the friction in the mechanism over theoperational range of the rotor. The test is repeated for different settingsof the offset mechanism, that translate to different values of maximumblade pitch. The measured mechanical power is then subtracted from thetotal power, yielding the aerodynamic power of the cycloidal rotor as afunction of rotational speed for each blade pitch angle.

Figure 26 shows the total mechanical power consumed by the three-bladed cycloidal rotor, and Fig. 27 shows the aerodynamic power obtainedafter subtracting the frictional power measured from the tare tests. It canbe seen that the total power is much larger than the aerodynamic power,especially at low blade pitch angles. This indicates an excessive amountof friction in the linkages of the four bar mechanism, as well as high dragon the rotating supports of the rotor blades. In addition, the frictionalpower shows a large increase at higher values of rotor speed. The designof the linkage mechanism for changing the pitch of the blades must berefined to minimize frictional losses and to successfully integrate thecycloidal rotor in a flight vehicle.

Figures 28 and 29 show the aerodynamic power consumed by thecycloidal rotor for the six-bladed and three-bladed cases. Predictions ofpower consumed are plotted for comparison. It can be seen that the ex-perimental power consumed is higher than the predicted values at higher


0

4

8

12

0 400 800 1200

RPM

Pow

er (

W)

10o

20o

30o

40o

Fig. 26. Total power consumed by the three-bladed cycloidal rotor asa function of blade pitch angle.

0

4

8

12

0 400 800 1200

RPM

Pow

er (

W)

10o20

o

30o

40o

Fig. 27. Aerodynamic power consumed by the three-bladed cycloidalrotor as a function of blade pitch angle.

rotational speeds and is lower than predictions at lower rotational speeds.In general the power predictions do not agree with experimental resultsas well as the thrust predictions, however, the correlation is much betterat higher rotational speeds. The errors may be due to incorrect constantssuch as CDo and e, as well as nonideal interaction between the blades,that is not captured by the analysis.

Comparison of the efficiency of the cycloidal rotorand a conventional rotor

To assess the potential of the cycloidal rotor concept, its hovering per-formance must be compared to that of a conventional rotor. A commonlyused metric of hover performance is the rotor figure of merit. The idealpower consumed depends on the disk area of the rotor. For a conventionalrotor, this area is clearly defined, however, for a cycloidal rotor, the diskarea is somewhat ambiguous. For the nondimensionalization discussed

0 200 400 600 800 1000 1200−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

RPM

Cp

Theory, pitch = 10o

Theory, pitch = 20o

Theory, pitch = 30o




Theory, pitch = 40o


Fig. 28. Aerodynamic power consumed by the six-bladed cycloidalrotor as a function of blade pitch angle and rpm.

0 200 400 600 800 1000 1200

RPM

Cp









0

0.02

0.04

0.06

0.08

0.1

0.12

−0.02

Fig. 29. Aerodynamic power consumed by the three-bladed cycloidalrotor as a function of blade pitch angle and rpm.

above, the reference area was taken to be the swept area, which is thesurface area of the cylinder described by the rotating blades. The diskarea of the cycloidal rotor could also be considered as the rectangulararea obtained by the projection of the rotor onto a horizontal plane. Inaddition, the figure of merit is typically plotted as a function of bladeloading CT/σ , which depends on rotor solidity σ , and is a measure ofthe mean lift coefficient CL of the rotor blade. In the case of a cycloidalrotor, the rotor solidity is not clearly defined. One way to define solidityis based on the swept area of the rotor blades, yielding

σs = blade area

rotor area= Nbc

2π R(27)

where Nb is the number of blades, c is the blade chord, and R is the rotorradius. Based on this definition of reference area, the blade loading ofthe cycloidal rotor can be derived as

CT

σ= CL

2(swept area) (28)


Another way is to define solidity based on the projected area. However,as the projected area of each blade depends on its azimuthal location, atime averaged blade area, Ab can be defined as follows:

Ab = Nbb1

π/2

π/2∫0

c cos ψ dψ = 2cbNb

π(29)

where c cos ψ is the projected chord of each blade at an azimuthal angleψ . From this mean blade area, the solidity is

σp = Nbc

π R(30)

Using this value of solidity and the projected area as the reference area,

CT

σ= πCL

4(projected area) (31)

Note that for a conventional rotor,

CT

σ= CL

6(32)

It can be seen that the comparison of the cycloidal rotor and conventionalrotor on the basis of figure of merit is dependent on the choice of anappropriate reference area. Therefore, a more physical metric is requiredas a basis for comparison.

From a practical viewpoint, the largest physical dimension is the mostimportant constraint in the design of a micro aerial vehicle. As the rotoris typically sized to occupy as much as possible of the allowable vehicledimension, a comparison of the performance of different lifting rotorscan be made based on a constant rotor dimension. In the case of a con-ventional rotor, the critical rotor dimension is the rotor diameter, and inthe case of a cycloidal rotor, it is the rotor span. For a given lifting rotor,the most important metric is the thrust produced for a unit input power(power loading). In addition, the absolute value of thrust produced is alsoimportant to be able to carry the maximum payload. Therefore, having atarget weight and payload, the best rotor is the one with highest powerloading at a given thrust, while fitting within a specified dimension.

To perform this comparison, the power loading of the cycloidal rotorwas measured and compared to that of a conventional two-bladed rotorwith a diameter equal to the span of the cycloidal rotor. The relevantparameters of the conventional rotor used in the comparison are providedin Table 2. Construction and testing of the rotor was performed by Heinand Chopra (Ref. 5). Testing was performed up to a blade tip Reynoldsnumber of approximately 40,000.

The power loadings of the three-bladed and six-bladed cycloidal rotorare shown in Figs. 30 and 31, respectively. It can be seen that the six-bladed rotor has a higher power loading at a given value of thrust. In addi-tion, the power loading is high at low values of thrust and decreases to anasymptote of about 25 g/W at high values of thrust. Both the three-bladedrotor and the six-bladed rotor asymptote to approximately the same valueof power loading at high thrust levels. Figure 32 shows a comparison ofthe power loading of the conventional rotor and the six-bladed cycloidalrotor. Note that the power loading of the conventional rotor corresponds

Table 2. Parameters of the conventional rotor

Parameter Value

Diameter 6 inchesChord 0.787 inchAirfoil camber 7%Airfoil thickness 2.75%

0

100

200

300

400

500

0 10 20 30 40 50 60

Thrust (g)

Thr

ust/

pow

er (

g/W

)

10o

20o

30o

40o

Fig. 30. Power loading of a three-bladed cycloidal rotor as a functionof rotor thrust, for different blade pitch angles.

0

100

200

300

400

500

0 10 20 30 40 50 60

Thrust (g)

Thr

ust/

pow

er (

g/W

)

10o

20o

30o

40o

Fig. 31. Power loading of a six-bladed cycloidal rotor as a functionof rotor thrust, for different blade pitch angles.

to an optimized rotor, with a best case figure of merit of around 0.55. Thedashed lines represent curves of constant collective for the conventionalrotor, and the shaded symbols represent the cycloidal rotor at differentblade pitch angles. The power loading of the conventional rotor increaseswith increasing collective but is still less than that of the cycloidal rotorat blade pitch angles of 30 and 40. It can also be seen that the conven-tional rotor can produce higher maximum thrust. However, the maximumrpm of the cycloidal rotor was limited in the test setup by mechanicalconsiderations, which limited the maximum thrust produced.

Conceptual Design of a Cyclo-MAV

Based on the experimental results, a paper study was conducted to de-termine the feasibility of implementing the cycloidal propulsion concepton a micro air vehicle. A vehicle using two cycloidal rotors of the samedimensions as tested in the current work, was designed using CATIA.The complete vehicle design is pictured in Fig. 33.

Blades are to be constructed with a foam core covered by a carbon fiberskin, and with a carbon rod spar to stiffen the blade against the significanttransverse centrifugal blade loading inherent in the cycloidal design. Theblades will be attached at one end to a three-arm frame fabricated fromcarbon fiber; at the other end, the blades will be held together by a carbon


0

10

20

30

40

50

0 10 20 30 40 50 60

Thrust (g)

Thr

ust/

pow

er (

g/W

)

Increasing rotor collective

Pitch angle 10o

Pitch angle 20o

Pitch angle 30o

Pitch angle 40o

Conventional rotor

Fig. 32. Comparison of power loading of a cycloidal rotor and aconventional rotor.

ring. This design would eliminate a considerable amount of weight overthe previous configuration, while still limiting the bending moment ofthe blade to acceptable levels.

Rotors will utilize a fixed pitch offset mechanism to achieve the re-quired change in blade pitch angle (Fig. 34). Although a variable pitchmechanism was used on the experimental rotor, a fixed pitch design canbe made much lighter. The mechanism will be set such that the maximumpitch angle of the blades is ±30.

Directional control of the vehicle will be achieved by rotating thedriveshaft of each rotor, which will change the azimuthal location of theoffset mechanism. The rotor driveshafts, both coincident with shaft bear-ings, will allow the rotors to rotate freely in any direction. The controlmechanism will consist of two small servos, mounted between the ro-tors. Actuation of the servos, which will be connected to the driveshaftthrough a linkage arrangement, would rotate the entire rotor, changingthe direction of thrust.

Fig. 33. Conceptual cycloidal rotor MAV.

Fig. 34. Fixed pitch offset mechanism.

The electronics package and payload will be positioned below and aftof the rotor axes such that their weight, in conjunction with an appropriatefuselage attitude, would provide the necessary anti-torque to trim thevehicle. This setup would eliminate the need for an additional devicefor torque compensation and its accompanying weight penalty. A weightbreakdown of the vehicle components is provided in Table 3, comparedto the weight breakdown of a single rotor MAV (Ref. 1) of the sametotal weight. Note that the increased rotor weight of the cyclo-MAV iscompensated for by a lower structure weight compared to the case of thesingle rotor MAV.

Based on the results from the paper study, the rotors on the cyclo-MAV will require a minimum rotational speed of 1650 rpm to achieve thenecessary thrust of 125 g per rotor. A speed of 1875 rpm should provideenough additional thrust for propulsion and control. The main drawback


Table 3. Component breakdown of cyclo-MAV compared with singlerotor MAV (Ref. 1)

Cyclo-MAV Single Rotor MAV

Component Weight (g) % Total Weight (g) % Total

Electronics and servos 38 15.3 38 15.9Li-Po battery (700 mAh) 53.3 21.4 53.3 22.2Motors 47.8 19.3 52.7 22Rotor system 91.3 37.0 26.4 11Structure 18.5 7.49 69.2 28.9Total 248.9 100 239.6 100

of the cyclo-MAV is the complexity of the mechanical linkages, as wellas the increased rotor mass. In addition, the present configuration is onlysuited for hover, and further research must be performed to investigatethe forward flight characteristics of such a vehicle. The final evaluationbetween the cyclo-MAV and a conventional single or coaxial rotor MAVmust involve all the aspects of the vehicle configuration, for example, thecyclo-MAV described above has a total span slightly more than that oftwo cycloidal rotors, while a conventional single or coaxial rotor MAVwill have a total rotor diameter that will depend upon the size of tail rotor,and numerous other factors.

Conclusions and Future Work

A prototype cycloidal rotor of diameter 6 inches and span 6 inches wasconstructed and tested on a test rig capable of measuring thrust, torque androtational speed. A theory was developed to predict the performance ofthe rotor, based on a streamtube momentum theory model in conjunctionwith a formulation of Wagner’s function to account for unsteady aerody-namic effects. The main assumptions in the analysis were to neglect anyinfluence of blades on each other, to consider equal thrust produced bythe upper and lower halves of the rotor, and to assume uniform inflow onthe rotor blades.

Thrust and power were determined as a function of rotational speedand blade pitch angle. Thrust increased with the square of rotationalspeed, while power increased with the cube of rpm. No dramatic reductionin thrust was measured as blade pitch angle was increased up to 40,indicating that dynamic stall may play a role in the operation of thecycloidal blade system. Tests were conducted on both a six-bladed rotorand a three-bladed rotor. The six-bladed rotor was observed to produceonly 30% more thrust than the three-bladed case at the same rpm andcollective setting.

Predictions of the direction of the thrust vector as a function of eccen-tricity of the four bar linkage correlated well with measurements. Thrustpredictions matched well with experiment for the three-bladed rotor, butwere less accurate for the six-bladed rotor. This could be a result of inter-action between the blades, which was neglected in the analysis. Tare testsrevealed that a major component of the mechanical power consumed bythe prototype cycloidal rotor was caused by friction, especially in thefour bar linkage mechanism. Power predictions were satisfactory only athigher rotational speeds and were in general poor at lower speeds andhigh blade pitch angles. Compared to a conventional rotor of the samediameter, a higher power loading was observed, especially at low val-ues of thrust. The power loading of both the three-bladed rotor and thesix-bladed rotor decreased with increasing thrust and leveled off at ap-proximately 25 g/W. Note that the power loading was calculated basedonly on the aerodynamic power of the cycloidal rotor.

An MAV utilizing cycloidal rotors was modeled and optimized forlow weight. The complete vehicle, including electronics and battery,

weighed approximately 250 g. Based on predictions, the rotors mustrotate at 1650 rpm for the vehicle to produce sufficient thrust. From thepresent work, it appears that while the cycloidal blade system is a viableconfiguration for a micro air vehicle, the efficiency of the system is highlydependent on the mechanical design and on minimizing the friction inthe linkages. The complexity and number of parts of the design are alsosubjects of consideration.

Future work involves optimization of the design to maximize its use-fulness. Previous research has shown that the NACA 0012 is extremelysensitive to variations in Reynolds number or turbulence, and is unsuit-able for Reynolds numbers less than 50,000. Blades with larger chordswould increase Reynolds number and may prove beneficial, althoughany benefits may be offset by the increase in solidity of the rotor, whichdecreases performance. In addition airfoil profile better suited to lowReynolds number operation could be explored.

Computational fluid dynamics (CFD) analysis would not only be use-ful in validating existing experimental and theoretical results, but wouldprovide a good means of understanding the flow conditions around therotor. Although cascade aerodynamics does not appear to have a sig-nificant effect on the model, it was apparent from the data that someinteractions between blades and blade wakes were taking place in thesix-bladed configuration.

Finally, it must be remembered that the mechanism currently usedto provide periodic changes in blade pitch is suitable only for hoveringconditions. An investigation of the blade motions at various forward flightspeeds, and the mechanisms needed for producing them, must be carriedout. Individual blade control, while probably the optimal configuration,would be difficult to implement on a small vehicle and would incur asignificant weight penalty. A series of cams, each optimized for differentflight speeds may prove to be a workable solution. The efficiency andhandling of a cycloidal rotor micro air vehicle must then be determinedthrough systematic experiments.

Acknowledgments

This research was carried out under the Multidisciplinary UniversityResearch Initiative (MURI) grant W911NF0410176 from the Army Re-search Office with Dr. Tom Doligalski as Technical Monitor.

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Documents

Hover Performance of a Cycloidal Rotor for a Micro Air Vehiclesites.utexas.edu/sirohi/files/2017/07/010_parsons07_jahs.pdf · 2017. 7. 24. · much higher viscous drag than conventional